On the exact Maxwell evolution equation of resonator dynamics
In a recent publication [Opt. Express 32, 20904 (2024)], the accuracy of the main evolution equation that governs resonator dynamics in the coupled-mode theory (CMT) was questioned. The study concluded that the driving force is proportional to the temporal derivative of the excitation field rather t...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2025-01-01
|
| Series: | Journal of the European Optical Society-Rapid Publications |
| Subjects: | |
| Online Access: | https://jeos.edpsciences.org/articles/jeos/full_html/2025/01/jeos20240069/jeos20240069.html |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206543947137024 |
|---|---|
| author | Wu Tong Zarouf Rachid Lalanne Philippe |
| author_facet | Wu Tong Zarouf Rachid Lalanne Philippe |
| author_sort | Wu Tong |
| collection | DOAJ |
| description | In a recent publication [Opt. Express 32, 20904 (2024)], the accuracy of the main evolution equation that governs resonator dynamics in the coupled-mode theory (CMT) was questioned. The study concluded that the driving force is proportional to the temporal derivative of the excitation field rather than the excitation field itself. This conclusion was reached with a derivation of an “exact” Maxwell evolution (EME) equation obtained directly from Maxwell’s equations, which was further supported by extensive numerical tests. Hereafter, we argue that the original derivation lacks mathematical rigor. We present a direct and rigorous derivation that establishes a solid mathematical foundation for the EME equation. This new approach clarifies the origin of the temporal derivative in the excitation term of CMT and elucidates the approximations present in the classical CMT evolution equation through a straightforward argument. |
| format | Article |
| id | doaj-art-115ece40e1f84729a05ce2ebf87ac38b |
| institution | Kabale University |
| issn | 1990-2573 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | Journal of the European Optical Society-Rapid Publications |
| spelling | doaj-art-115ece40e1f84729a05ce2ebf87ac38b2025-02-07T08:22:54ZengEDP SciencesJournal of the European Optical Society-Rapid Publications1990-25732025-01-01211510.1051/jeos/2024048jeos20240069On the exact Maxwell evolution equation of resonator dynamicsWu Tong0Zarouf Rachid1Lalanne Philippe2https://orcid.org/0000-0003-1979-2290Laboratoire Photonique, Numérique et Nanosciences (LP2N), IOGS – Université de Bordeaux-CNRSAix-Marseille Université, Laboratoire ADEF, Campus Universitaire de Saint-JérômeLaboratoire Photonique, Numérique et Nanosciences (LP2N), IOGS – Université de Bordeaux-CNRSIn a recent publication [Opt. Express 32, 20904 (2024)], the accuracy of the main evolution equation that governs resonator dynamics in the coupled-mode theory (CMT) was questioned. The study concluded that the driving force is proportional to the temporal derivative of the excitation field rather than the excitation field itself. This conclusion was reached with a derivation of an “exact” Maxwell evolution (EME) equation obtained directly from Maxwell’s equations, which was further supported by extensive numerical tests. Hereafter, we argue that the original derivation lacks mathematical rigor. We present a direct and rigorous derivation that establishes a solid mathematical foundation for the EME equation. This new approach clarifies the origin of the temporal derivative in the excitation term of CMT and elucidates the approximations present in the classical CMT evolution equation through a straightforward argument.https://jeos.edpsciences.org/articles/jeos/full_html/2025/01/jeos20240069/jeos20240069.htmlcoupled-mode theoryelectromagnetic resonancequasinormal moderesonant scattering |
| spellingShingle | Wu Tong Zarouf Rachid Lalanne Philippe On the exact Maxwell evolution equation of resonator dynamics Journal of the European Optical Society-Rapid Publications coupled-mode theory electromagnetic resonance quasinormal mode resonant scattering |
| title | On the exact Maxwell evolution equation of resonator dynamics |
| title_full | On the exact Maxwell evolution equation of resonator dynamics |
| title_fullStr | On the exact Maxwell evolution equation of resonator dynamics |
| title_full_unstemmed | On the exact Maxwell evolution equation of resonator dynamics |
| title_short | On the exact Maxwell evolution equation of resonator dynamics |
| title_sort | on the exact maxwell evolution equation of resonator dynamics |
| topic | coupled-mode theory electromagnetic resonance quasinormal mode resonant scattering |
| url | https://jeos.edpsciences.org/articles/jeos/full_html/2025/01/jeos20240069/jeos20240069.html |
| work_keys_str_mv | AT wutong ontheexactmaxwellevolutionequationofresonatordynamics AT zaroufrachid ontheexactmaxwellevolutionequationofresonatordynamics AT lalannephilippe ontheexactmaxwellevolutionequationofresonatordynamics |